Neuroscientists have debated for centuries whether some regions of the human brain are selectively engaged in specific high-level mental functions or whether, instead, cognition is implemented in multifunctional brain regions. For the critical case of language, conflicting answers arise from the neuropsychological literature, which features striking dissociations between deficits in linguistic and nonlinguistic abilities, vs. the neuroimaging literature, which has argued for overlap between activations for linguistic and nonlinguistic processes, including arithmetic, domain general abilities like cognitive control, and music. Here, we use functional MRI to define classic language regions functionally in each subject individually and then examine the response of these regions to the nonlinguistic functions most commonly argued to engage these regions: arithmetic, working memory, cognitive control, and music. We find little or no response in language regions to these nonlinguistic functions. These data support a clear distinction between language and other cognitive processes, resolving the prior conflict between the neuropsychological and neuroimaging literatures.